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a(n) = (12n+4)^9.
0

%I #15 Dec 30 2024 22:44:16

%S 262144,68719476736,10578455953408,262144000000000,2779905883635712,

%T 18014398509481984,84590643846578176,316478381828866048,

%U 1000000000000000000,2773078757450186752,6930988311686938624,15916595351771938816,34068690316840665088,68719476736000000000

%N a(n) = (12n+4)^9.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F From _Amiram Eldar_, Jul 14 2024: (Start)

%F a(n) = A001017(A017569(n)) = A017569(n)^9.

%F a(n) = 262144 * A016785(n).

%F Sum_{n>=0} 1/a(n) = 809*Pi^9/(7313988648960*sqrt(3)) + 9841*zeta(9)/5159780352. (End)

%t (12*Range[0,30]+4)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{262144,68719476736,10578455953408,262144000000000,2779905883635712,18014398509481984,84590643846578176,316478381828866048,1000000000000000000,2773078757450186752},40] (* _Harvey P. Dale_, Sep 07 2018 *)

%Y Cf. A001017, A013667, A016785, A017569.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Amiram Eldar_, Jul 14 2024